Usually it works like this. Either you contact or get contacted by the company wanting an Instagram promotion. Depending on the size of the company and budget, they may attach a contract or Instagram ambassador agreement. Companies that are familiar with promotions will often send you an Instagram ambassador promo packages like these:
Since Facebook doesn't talk much about money they make off Instagram, there are many speculations made. The most recent being MofettNathanson, an analyst firm which predicted today that Instagram will bring in $600 million in revenue over the next year. This number is only expected to increase within the next two to three years with revenues forecast at $1.8 billion.